LMFDB - Dirichlet character orbit 2349.bt

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2349, base_ring=CyclotomicField(378)) M = H._module chi = DirichletCharacter(H, M([161,297])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(5,2349)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$2349$
Conductor:	$2349$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$378$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{189})$
Fixed field:	Number field defined by a degree 378 polynomial (not computed)

First 31 of 108 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{2349}(5,\cdot)$	$-1$	$1$	$e\left(\frac{40}{189}\right)$	$e\left(\frac{80}{189}\right)$	$e\left(\frac{31}{378}\right)$	$e\left(\frac{46}{189}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{37}{126}\right)$	$e\left(\frac{34}{189}\right)$	$e\left(\frac{104}{189}\right)$	$e\left(\frac{86}{189}\right)$	$e\left(\frac{160}{189}\right)$
$\chi_{2349}(38,\cdot)$	$-1$	$1$	$e\left(\frac{50}{189}\right)$	$e\left(\frac{100}{189}\right)$	$e\left(\frac{275}{378}\right)$	$e\left(\frac{152}{189}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{125}{126}\right)$	$e\left(\frac{137}{189}\right)$	$e\left(\frac{130}{189}\right)$	$e\left(\frac{13}{189}\right)$	$e\left(\frac{11}{189}\right)$
$\chi_{2349}(92,\cdot)$	$-1$	$1$	$e\left(\frac{5}{189}\right)$	$e\left(\frac{10}{189}\right)$	$e\left(\frac{311}{378}\right)$	$e\left(\frac{53}{189}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{107}{126}\right)$	$e\left(\frac{146}{189}\right)$	$e\left(\frac{13}{189}\right)$	$e\left(\frac{58}{189}\right)$	$e\left(\frac{20}{189}\right)$
$\chi_{2349}(122,\cdot)$	$-1$	$1$	$e\left(\frac{37}{189}\right)$	$e\left(\frac{74}{189}\right)$	$e\left(\frac{109}{378}\right)$	$e\left(\frac{52}{189}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{61}{126}\right)$	$e\left(\frac{22}{189}\right)$	$e\left(\frac{134}{189}\right)$	$e\left(\frac{89}{189}\right)$	$e\left(\frac{148}{189}\right)$
$\chi_{2349}(149,\cdot)$	$-1$	$1$	$e\left(\frac{136}{189}\right)$	$e\left(\frac{83}{189}\right)$	$e\left(\frac{181}{378}\right)$	$e\left(\frac{43}{189}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{25}{126}\right)$	$e\left(\frac{40}{189}\right)$	$e\left(\frac{89}{189}\right)$	$e\left(\frac{179}{189}\right)$	$e\left(\frac{166}{189}\right)$
$\chi_{2349}(158,\cdot)$	$-1$	$1$	$e\left(\frac{34}{189}\right)$	$e\left(\frac{68}{189}\right)$	$e\left(\frac{187}{378}\right)$	$e\left(\frac{58}{189}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{85}{126}\right)$	$e\left(\frac{10}{189}\right)$	$e\left(\frac{164}{189}\right)$	$e\left(\frac{92}{189}\right)$	$e\left(\frac{136}{189}\right)$
$\chi_{2349}(167,\cdot)$	$-1$	$1$	$e\left(\frac{67}{189}\right)$	$e\left(\frac{134}{189}\right)$	$e\left(\frac{85}{378}\right)$	$e\left(\frac{181}{189}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{73}{126}\right)$	$e\left(\frac{142}{189}\right)$	$e\left(\frac{23}{189}\right)$	$e\left(\frac{59}{189}\right)$	$e\left(\frac{79}{189}\right)$
$\chi_{2349}(209,\cdot)$	$-1$	$1$	$e\left(\frac{65}{189}\right)$	$e\left(\frac{130}{189}\right)$	$e\left(\frac{263}{378}\right)$	$e\left(\frac{122}{189}\right)$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{5}{126}\right)$	$e\left(\frac{8}{189}\right)$	$e\left(\frac{169}{189}\right)$	$e\left(\frac{187}{189}\right)$	$e\left(\frac{71}{189}\right)$
$\chi_{2349}(212,\cdot)$	$-1$	$1$	$e\left(\frac{43}{189}\right)$	$e\left(\frac{86}{189}\right)$	$e\left(\frac{331}{378}\right)$	$e\left(\frac{40}{189}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{13}{126}\right)$	$e\left(\frac{46}{189}\right)$	$e\left(\frac{74}{189}\right)$	$e\left(\frac{83}{189}\right)$	$e\left(\frac{172}{189}\right)$
$\chi_{2349}(236,\cdot)$	$-1$	$1$	$e\left(\frac{164}{189}\right)$	$e\left(\frac{139}{189}\right)$	$e\left(\frac{335}{378}\right)$	$e\left(\frac{113}{189}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{95}{126}\right)$	$e\left(\frac{26}{189}\right)$	$e\left(\frac{124}{189}\right)$	$e\left(\frac{88}{189}\right)$	$e\left(\frac{89}{189}\right)$
$\chi_{2349}(245,\cdot)$	$-1$	$1$	$e\left(\frac{125}{189}\right)$	$e\left(\frac{61}{189}\right)$	$e\left(\frac{215}{378}\right)$	$e\left(\frac{2}{189}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{29}{126}\right)$	$e\left(\frac{59}{189}\right)$	$e\left(\frac{136}{189}\right)$	$e\left(\frac{127}{189}\right)$	$e\left(\frac{122}{189}\right)$
$\chi_{2349}(254,\cdot)$	$-1$	$1$	$e\left(\frac{32}{189}\right)$	$e\left(\frac{64}{189}\right)$	$e\left(\frac{365}{378}\right)$	$e\left(\frac{188}{189}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{17}{126}\right)$	$e\left(\frac{65}{189}\right)$	$e\left(\frac{121}{189}\right)$	$e\left(\frac{31}{189}\right)$	$e\left(\frac{128}{189}\right)$
$\chi_{2349}(266,\cdot)$	$-1$	$1$	$e\left(\frac{187}{189}\right)$	$e\left(\frac{185}{189}\right)$	$e\left(\frac{367}{378}\right)$	$e\left(\frac{130}{189}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{121}{126}\right)$	$e\left(\frac{55}{189}\right)$	$e\left(\frac{146}{189}\right)$	$e\left(\frac{128}{189}\right)$	$e\left(\frac{181}{189}\right)$
$\chi_{2349}(299,\cdot)$	$-1$	$1$	$e\left(\frac{134}{189}\right)$	$e\left(\frac{79}{189}\right)$	$e\left(\frac{359}{378}\right)$	$e\left(\frac{173}{189}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{83}{126}\right)$	$e\left(\frac{95}{189}\right)$	$e\left(\frac{46}{189}\right)$	$e\left(\frac{118}{189}\right)$	$e\left(\frac{158}{189}\right)$
$\chi_{2349}(353,\cdot)$	$-1$	$1$	$e\left(\frac{89}{189}\right)$	$e\left(\frac{178}{189}\right)$	$e\left(\frac{17}{378}\right)$	$e\left(\frac{74}{189}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{65}{126}\right)$	$e\left(\frac{104}{189}\right)$	$e\left(\frac{118}{189}\right)$	$e\left(\frac{163}{189}\right)$	$e\left(\frac{167}{189}\right)$
$\chi_{2349}(383,\cdot)$	$-1$	$1$	$e\left(\frac{184}{189}\right)$	$e\left(\frac{179}{189}\right)$	$e\left(\frac{67}{378}\right)$	$e\left(\frac{136}{189}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{19}{126}\right)$	$e\left(\frac{43}{189}\right)$	$e\left(\frac{176}{189}\right)$	$e\left(\frac{131}{189}\right)$	$e\left(\frac{169}{189}\right)$
$\chi_{2349}(410,\cdot)$	$-1$	$1$	$e\left(\frac{94}{189}\right)$	$e\left(\frac{188}{189}\right)$	$e\left(\frac{139}{378}\right)$	$e\left(\frac{127}{189}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{109}{126}\right)$	$e\left(\frac{61}{189}\right)$	$e\left(\frac{131}{189}\right)$	$e\left(\frac{32}{189}\right)$	$e\left(\frac{187}{189}\right)$
$\chi_{2349}(419,\cdot)$	$-1$	$1$	$e\left(\frac{181}{189}\right)$	$e\left(\frac{173}{189}\right)$	$e\left(\frac{145}{378}\right)$	$e\left(\frac{142}{189}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{43}{126}\right)$	$e\left(\frac{31}{189}\right)$	$e\left(\frac{17}{189}\right)$	$e\left(\frac{134}{189}\right)$	$e\left(\frac{157}{189}\right)$
$\chi_{2349}(428,\cdot)$	$-1$	$1$	$e\left(\frac{25}{189}\right)$	$e\left(\frac{50}{189}\right)$	$e\left(\frac{43}{378}\right)$	$e\left(\frac{76}{189}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{31}{126}\right)$	$e\left(\frac{163}{189}\right)$	$e\left(\frac{65}{189}\right)$	$e\left(\frac{101}{189}\right)$	$e\left(\frac{100}{189}\right)$
$\chi_{2349}(470,\cdot)$	$-1$	$1$	$e\left(\frac{149}{189}\right)$	$e\left(\frac{109}{189}\right)$	$e\left(\frac{347}{378}\right)$	$e\left(\frac{143}{189}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{89}{126}\right)$	$e\left(\frac{155}{189}\right)$	$e\left(\frac{85}{189}\right)$	$e\left(\frac{103}{189}\right)$	$e\left(\frac{29}{189}\right)$
$\chi_{2349}(473,\cdot)$	$-1$	$1$	$e\left(\frac{1}{189}\right)$	$e\left(\frac{2}{189}\right)$	$e\left(\frac{289}{378}\right)$	$e\left(\frac{124}{189}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{97}{126}\right)$	$e\left(\frac{67}{189}\right)$	$e\left(\frac{116}{189}\right)$	$e\left(\frac{125}{189}\right)$	$e\left(\frac{4}{189}\right)$
$\chi_{2349}(497,\cdot)$	$-1$	$1$	$e\left(\frac{59}{189}\right)$	$e\left(\frac{118}{189}\right)$	$e\left(\frac{41}{378}\right)$	$e\left(\frac{134}{189}\right)$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{53}{126}\right)$	$e\left(\frac{173}{189}\right)$	$e\left(\frac{40}{189}\right)$	$e\left(\frac{4}{189}\right)$	$e\left(\frac{47}{189}\right)$
$\chi_{2349}(506,\cdot)$	$-1$	$1$	$e\left(\frac{20}{189}\right)$	$e\left(\frac{40}{189}\right)$	$e\left(\frac{299}{378}\right)$	$e\left(\frac{23}{189}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{113}{126}\right)$	$e\left(\frac{17}{189}\right)$	$e\left(\frac{52}{189}\right)$	$e\left(\frac{43}{189}\right)$	$e\left(\frac{80}{189}\right)$
$\chi_{2349}(515,\cdot)$	$-1$	$1$	$e\left(\frac{116}{189}\right)$	$e\left(\frac{43}{189}\right)$	$e\left(\frac{71}{378}\right)$	$e\left(\frac{20}{189}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{101}{126}\right)$	$e\left(\frac{23}{189}\right)$	$e\left(\frac{37}{189}\right)$	$e\left(\frac{136}{189}\right)$	$e\left(\frac{86}{189}\right)$
$\chi_{2349}(527,\cdot)$	$-1$	$1$	$e\left(\frac{145}{189}\right)$	$e\left(\frac{101}{189}\right)$	$e\left(\frac{325}{378}\right)$	$e\left(\frac{25}{189}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{79}{126}\right)$	$e\left(\frac{76}{189}\right)$	$e\left(\frac{188}{189}\right)$	$e\left(\frac{170}{189}\right)$	$e\left(\frac{13}{189}\right)$
$\chi_{2349}(560,\cdot)$	$-1$	$1$	$e\left(\frac{29}{189}\right)$	$e\left(\frac{58}{189}\right)$	$e\left(\frac{65}{378}\right)$	$e\left(\frac{5}{189}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{41}{126}\right)$	$e\left(\frac{53}{189}\right)$	$e\left(\frac{151}{189}\right)$	$e\left(\frac{34}{189}\right)$	$e\left(\frac{116}{189}\right)$
$\chi_{2349}(614,\cdot)$	$-1$	$1$	$e\left(\frac{173}{189}\right)$	$e\left(\frac{157}{189}\right)$	$e\left(\frac{101}{378}\right)$	$e\left(\frac{95}{189}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{23}{126}\right)$	$e\left(\frac{62}{189}\right)$	$e\left(\frac{34}{189}\right)$	$e\left(\frac{79}{189}\right)$	$e\left(\frac{125}{189}\right)$
$\chi_{2349}(644,\cdot)$	$-1$	$1$	$e\left(\frac{142}{189}\right)$	$e\left(\frac{95}{189}\right)$	$e\left(\frac{25}{378}\right)$	$e\left(\frac{31}{189}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{103}{126}\right)$	$e\left(\frac{64}{189}\right)$	$e\left(\frac{29}{189}\right)$	$e\left(\frac{173}{189}\right)$	$e\left(\frac{1}{189}\right)$
$\chi_{2349}(671,\cdot)$	$-1$	$1$	$e\left(\frac{52}{189}\right)$	$e\left(\frac{104}{189}\right)$	$e\left(\frac{97}{378}\right)$	$e\left(\frac{22}{189}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{67}{126}\right)$	$e\left(\frac{82}{189}\right)$	$e\left(\frac{173}{189}\right)$	$e\left(\frac{74}{189}\right)$	$e\left(\frac{19}{189}\right)$
$\chi_{2349}(680,\cdot)$	$-1$	$1$	$e\left(\frac{139}{189}\right)$	$e\left(\frac{89}{189}\right)$	$e\left(\frac{103}{378}\right)$	$e\left(\frac{37}{189}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{1}{126}\right)$	$e\left(\frac{52}{189}\right)$	$e\left(\frac{59}{189}\right)$	$e\left(\frac{176}{189}\right)$	$e\left(\frac{178}{189}\right)$
$\chi_{2349}(689,\cdot)$	$-1$	$1$	$e\left(\frac{172}{189}\right)$	$e\left(\frac{155}{189}\right)$	$e\left(\frac{1}{378}\right)$	$e\left(\frac{160}{189}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{115}{126}\right)$	$e\left(\frac{184}{189}\right)$	$e\left(\frac{107}{189}\right)$	$e\left(\frac{143}{189}\right)$	$e\left(\frac{121}{189}\right)$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Character	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{2349}(5,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{40}{189}\right)\)	\(e\left(\frac{80}{189}\right)\)	\(e\left(\frac{31}{378}\right)\)	\(e\left(\frac{46}{189}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{37}{126}\right)\)	\(e\left(\frac{34}{189}\right)\)	\(e\left(\frac{104}{189}\right)\)	\(e\left(\frac{86}{189}\right)\)	\(e\left(\frac{160}{189}\right)\)
\(\chi_{2349}(38,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{50}{189}\right)\)	\(e\left(\frac{100}{189}\right)\)	\(e\left(\frac{275}{378}\right)\)	\(e\left(\frac{152}{189}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{125}{126}\right)\)	\(e\left(\frac{137}{189}\right)\)	\(e\left(\frac{130}{189}\right)\)	\(e\left(\frac{13}{189}\right)\)	\(e\left(\frac{11}{189}\right)\)
\(\chi_{2349}(92,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{189}\right)\)	\(e\left(\frac{10}{189}\right)\)	\(e\left(\frac{311}{378}\right)\)	\(e\left(\frac{53}{189}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{107}{126}\right)\)	\(e\left(\frac{146}{189}\right)\)	\(e\left(\frac{13}{189}\right)\)	\(e\left(\frac{58}{189}\right)\)	\(e\left(\frac{20}{189}\right)\)
\(\chi_{2349}(122,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{189}\right)\)	\(e\left(\frac{74}{189}\right)\)	\(e\left(\frac{109}{378}\right)\)	\(e\left(\frac{52}{189}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{61}{126}\right)\)	\(e\left(\frac{22}{189}\right)\)	\(e\left(\frac{134}{189}\right)\)	\(e\left(\frac{89}{189}\right)\)	\(e\left(\frac{148}{189}\right)\)
\(\chi_{2349}(149,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{136}{189}\right)\)	\(e\left(\frac{83}{189}\right)\)	\(e\left(\frac{181}{378}\right)\)	\(e\left(\frac{43}{189}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{25}{126}\right)\)	\(e\left(\frac{40}{189}\right)\)	\(e\left(\frac{89}{189}\right)\)	\(e\left(\frac{179}{189}\right)\)	\(e\left(\frac{166}{189}\right)\)
\(\chi_{2349}(158,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{34}{189}\right)\)	\(e\left(\frac{68}{189}\right)\)	\(e\left(\frac{187}{378}\right)\)	\(e\left(\frac{58}{189}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{85}{126}\right)\)	\(e\left(\frac{10}{189}\right)\)	\(e\left(\frac{164}{189}\right)\)	\(e\left(\frac{92}{189}\right)\)	\(e\left(\frac{136}{189}\right)\)
\(\chi_{2349}(167,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{67}{189}\right)\)	\(e\left(\frac{134}{189}\right)\)	\(e\left(\frac{85}{378}\right)\)	\(e\left(\frac{181}{189}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{73}{126}\right)\)	\(e\left(\frac{142}{189}\right)\)	\(e\left(\frac{23}{189}\right)\)	\(e\left(\frac{59}{189}\right)\)	\(e\left(\frac{79}{189}\right)\)
\(\chi_{2349}(209,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{65}{189}\right)\)	\(e\left(\frac{130}{189}\right)\)	\(e\left(\frac{263}{378}\right)\)	\(e\left(\frac{122}{189}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{5}{126}\right)\)	\(e\left(\frac{8}{189}\right)\)	\(e\left(\frac{169}{189}\right)\)	\(e\left(\frac{187}{189}\right)\)	\(e\left(\frac{71}{189}\right)\)
\(\chi_{2349}(212,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{189}\right)\)	\(e\left(\frac{86}{189}\right)\)	\(e\left(\frac{331}{378}\right)\)	\(e\left(\frac{40}{189}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{13}{126}\right)\)	\(e\left(\frac{46}{189}\right)\)	\(e\left(\frac{74}{189}\right)\)	\(e\left(\frac{83}{189}\right)\)	\(e\left(\frac{172}{189}\right)\)
\(\chi_{2349}(236,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{164}{189}\right)\)	\(e\left(\frac{139}{189}\right)\)	\(e\left(\frac{335}{378}\right)\)	\(e\left(\frac{113}{189}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{95}{126}\right)\)	\(e\left(\frac{26}{189}\right)\)	\(e\left(\frac{124}{189}\right)\)	\(e\left(\frac{88}{189}\right)\)	\(e\left(\frac{89}{189}\right)\)
\(\chi_{2349}(245,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{125}{189}\right)\)	\(e\left(\frac{61}{189}\right)\)	\(e\left(\frac{215}{378}\right)\)	\(e\left(\frac{2}{189}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{29}{126}\right)\)	\(e\left(\frac{59}{189}\right)\)	\(e\left(\frac{136}{189}\right)\)	\(e\left(\frac{127}{189}\right)\)	\(e\left(\frac{122}{189}\right)\)
\(\chi_{2349}(254,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{32}{189}\right)\)	\(e\left(\frac{64}{189}\right)\)	\(e\left(\frac{365}{378}\right)\)	\(e\left(\frac{188}{189}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{17}{126}\right)\)	\(e\left(\frac{65}{189}\right)\)	\(e\left(\frac{121}{189}\right)\)	\(e\left(\frac{31}{189}\right)\)	\(e\left(\frac{128}{189}\right)\)
\(\chi_{2349}(266,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{187}{189}\right)\)	\(e\left(\frac{185}{189}\right)\)	\(e\left(\frac{367}{378}\right)\)	\(e\left(\frac{130}{189}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{121}{126}\right)\)	\(e\left(\frac{55}{189}\right)\)	\(e\left(\frac{146}{189}\right)\)	\(e\left(\frac{128}{189}\right)\)	\(e\left(\frac{181}{189}\right)\)
\(\chi_{2349}(299,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{134}{189}\right)\)	\(e\left(\frac{79}{189}\right)\)	\(e\left(\frac{359}{378}\right)\)	\(e\left(\frac{173}{189}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{83}{126}\right)\)	\(e\left(\frac{95}{189}\right)\)	\(e\left(\frac{46}{189}\right)\)	\(e\left(\frac{118}{189}\right)\)	\(e\left(\frac{158}{189}\right)\)
\(\chi_{2349}(353,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{89}{189}\right)\)	\(e\left(\frac{178}{189}\right)\)	\(e\left(\frac{17}{378}\right)\)	\(e\left(\frac{74}{189}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{65}{126}\right)\)	\(e\left(\frac{104}{189}\right)\)	\(e\left(\frac{118}{189}\right)\)	\(e\left(\frac{163}{189}\right)\)	\(e\left(\frac{167}{189}\right)\)
\(\chi_{2349}(383,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{184}{189}\right)\)	\(e\left(\frac{179}{189}\right)\)	\(e\left(\frac{67}{378}\right)\)	\(e\left(\frac{136}{189}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{19}{126}\right)\)	\(e\left(\frac{43}{189}\right)\)	\(e\left(\frac{176}{189}\right)\)	\(e\left(\frac{131}{189}\right)\)	\(e\left(\frac{169}{189}\right)\)
\(\chi_{2349}(410,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{94}{189}\right)\)	\(e\left(\frac{188}{189}\right)\)	\(e\left(\frac{139}{378}\right)\)	\(e\left(\frac{127}{189}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{109}{126}\right)\)	\(e\left(\frac{61}{189}\right)\)	\(e\left(\frac{131}{189}\right)\)	\(e\left(\frac{32}{189}\right)\)	\(e\left(\frac{187}{189}\right)\)
\(\chi_{2349}(419,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{181}{189}\right)\)	\(e\left(\frac{173}{189}\right)\)	\(e\left(\frac{145}{378}\right)\)	\(e\left(\frac{142}{189}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{43}{126}\right)\)	\(e\left(\frac{31}{189}\right)\)	\(e\left(\frac{17}{189}\right)\)	\(e\left(\frac{134}{189}\right)\)	\(e\left(\frac{157}{189}\right)\)
\(\chi_{2349}(428,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{189}\right)\)	\(e\left(\frac{50}{189}\right)\)	\(e\left(\frac{43}{378}\right)\)	\(e\left(\frac{76}{189}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{31}{126}\right)\)	\(e\left(\frac{163}{189}\right)\)	\(e\left(\frac{65}{189}\right)\)	\(e\left(\frac{101}{189}\right)\)	\(e\left(\frac{100}{189}\right)\)
\(\chi_{2349}(470,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{149}{189}\right)\)	\(e\left(\frac{109}{189}\right)\)	\(e\left(\frac{347}{378}\right)\)	\(e\left(\frac{143}{189}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{89}{126}\right)\)	\(e\left(\frac{155}{189}\right)\)	\(e\left(\frac{85}{189}\right)\)	\(e\left(\frac{103}{189}\right)\)	\(e\left(\frac{29}{189}\right)\)
\(\chi_{2349}(473,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{189}\right)\)	\(e\left(\frac{2}{189}\right)\)	\(e\left(\frac{289}{378}\right)\)	\(e\left(\frac{124}{189}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{97}{126}\right)\)	\(e\left(\frac{67}{189}\right)\)	\(e\left(\frac{116}{189}\right)\)	\(e\left(\frac{125}{189}\right)\)	\(e\left(\frac{4}{189}\right)\)
\(\chi_{2349}(497,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{189}\right)\)	\(e\left(\frac{118}{189}\right)\)	\(e\left(\frac{41}{378}\right)\)	\(e\left(\frac{134}{189}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{53}{126}\right)\)	\(e\left(\frac{173}{189}\right)\)	\(e\left(\frac{40}{189}\right)\)	\(e\left(\frac{4}{189}\right)\)	\(e\left(\frac{47}{189}\right)\)
\(\chi_{2349}(506,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{20}{189}\right)\)	\(e\left(\frac{40}{189}\right)\)	\(e\left(\frac{299}{378}\right)\)	\(e\left(\frac{23}{189}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{113}{126}\right)\)	\(e\left(\frac{17}{189}\right)\)	\(e\left(\frac{52}{189}\right)\)	\(e\left(\frac{43}{189}\right)\)	\(e\left(\frac{80}{189}\right)\)
\(\chi_{2349}(515,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{116}{189}\right)\)	\(e\left(\frac{43}{189}\right)\)	\(e\left(\frac{71}{378}\right)\)	\(e\left(\frac{20}{189}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{101}{126}\right)\)	\(e\left(\frac{23}{189}\right)\)	\(e\left(\frac{37}{189}\right)\)	\(e\left(\frac{136}{189}\right)\)	\(e\left(\frac{86}{189}\right)\)
\(\chi_{2349}(527,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{145}{189}\right)\)	\(e\left(\frac{101}{189}\right)\)	\(e\left(\frac{325}{378}\right)\)	\(e\left(\frac{25}{189}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{79}{126}\right)\)	\(e\left(\frac{76}{189}\right)\)	\(e\left(\frac{188}{189}\right)\)	\(e\left(\frac{170}{189}\right)\)	\(e\left(\frac{13}{189}\right)\)
\(\chi_{2349}(560,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{189}\right)\)	\(e\left(\frac{58}{189}\right)\)	\(e\left(\frac{65}{378}\right)\)	\(e\left(\frac{5}{189}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{41}{126}\right)\)	\(e\left(\frac{53}{189}\right)\)	\(e\left(\frac{151}{189}\right)\)	\(e\left(\frac{34}{189}\right)\)	\(e\left(\frac{116}{189}\right)\)
\(\chi_{2349}(614,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{173}{189}\right)\)	\(e\left(\frac{157}{189}\right)\)	\(e\left(\frac{101}{378}\right)\)	\(e\left(\frac{95}{189}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{23}{126}\right)\)	\(e\left(\frac{62}{189}\right)\)	\(e\left(\frac{34}{189}\right)\)	\(e\left(\frac{79}{189}\right)\)	\(e\left(\frac{125}{189}\right)\)
\(\chi_{2349}(644,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{142}{189}\right)\)	\(e\left(\frac{95}{189}\right)\)	\(e\left(\frac{25}{378}\right)\)	\(e\left(\frac{31}{189}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{103}{126}\right)\)	\(e\left(\frac{64}{189}\right)\)	\(e\left(\frac{29}{189}\right)\)	\(e\left(\frac{173}{189}\right)\)	\(e\left(\frac{1}{189}\right)\)
\(\chi_{2349}(671,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{52}{189}\right)\)	\(e\left(\frac{104}{189}\right)\)	\(e\left(\frac{97}{378}\right)\)	\(e\left(\frac{22}{189}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{67}{126}\right)\)	\(e\left(\frac{82}{189}\right)\)	\(e\left(\frac{173}{189}\right)\)	\(e\left(\frac{74}{189}\right)\)	\(e\left(\frac{19}{189}\right)\)
\(\chi_{2349}(680,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{139}{189}\right)\)	\(e\left(\frac{89}{189}\right)\)	\(e\left(\frac{103}{378}\right)\)	\(e\left(\frac{37}{189}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{1}{126}\right)\)	\(e\left(\frac{52}{189}\right)\)	\(e\left(\frac{59}{189}\right)\)	\(e\left(\frac{176}{189}\right)\)	\(e\left(\frac{178}{189}\right)\)
\(\chi_{2349}(689,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{172}{189}\right)\)	\(e\left(\frac{155}{189}\right)\)	\(e\left(\frac{1}{378}\right)\)	\(e\left(\frac{160}{189}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{115}{126}\right)\)	\(e\left(\frac{184}{189}\right)\)	\(e\left(\frac{107}{189}\right)\)	\(e\left(\frac{143}{189}\right)\)	\(e\left(\frac{121}{189}\right)\)

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First 31 of 108 characters in Galois orbit

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	2349.bt
Modulus	$2349$
Conductor	$2349$
Order	$378$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(2349\)
Conductor:	\(2349\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(378\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)